Cremona's table of elliptic curves

Curve 81685d1

81685 = 5 · 17 · 312



Data for elliptic curve 81685d1

Field Data Notes
Atkin-Lehner 5+ 17+ 31- Signs for the Atkin-Lehner involutions
Class 81685d Isogeny class
Conductor 81685 Conductor
∏ cp 4 Product of Tamagawa factors cp
deg 1313280 Modular degree for the optimal curve
Δ 913504765404296875 = 59 · 17 · 317 Discriminant
Eigenvalues -1 -1 5+  2  6  1 17+  2 Hecke eigenvalues for primes up to 20
Equation [1,1,1,-865881,306335044] [a1,a2,a3,a4,a6]
j 80896216567249/1029296875 j-invariant
L 1.1230116592132 L(r)(E,1)/r!
Ω 0.28075291822549 Real period
R 1 Regulator
r 0 Rank of the group of rational points
S 1 (Analytic) order of Ш
t 1 Number of elements in the torsion subgroup
Twists 2635a1 Quadratic twists by: -31


Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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